Healing/Tank on PS3 or PS4

[Niwashi]

however, if they are in your Enmity List, other words you used a action on the tank before they were put to sleep, then obviously you induce enmity. regardless if they are sleeping or not.

I don't think so. You'd retain whatever enmity you already had, but you don't induce any more enmity based on your actions while they're sleeping. Sleeping mobs will wake with whatever enmity they had as of the moment they fell asleep.